My boolean/difference operation didn't work
The modifiers are designed so you can change them later; if you changed the target object, it would change the effect. Similarly, if you delete the target object, it will remove the effect!

What you need to do is to apply the modifier. There should be an Apply button just beneath the 'add modifier' popup.

Note that this will make it impossible to remove the effect again later (except manually, of course), but if you're deleting the plane anyway, it should be what you need.